C₈×D₂₈ #89458

order	448
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

C₈×D₂₈

Fitting	C₄×C₇×C₈ ⋊ C₂
Sylow	C₇ ⋊ C₈×D₄

134 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 224

A minimal faithful permutation representation — 3 generators on 19 points:

(1,2,4,6,7,5,3)(8,9,10,11);(2,3)(4,5)(6,7)(9,11);(12,13,14,16,15,17,18,19)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 220);